Balsa Wood Surfboards

Like Ed said Basswood would be better. Also to seaal it, if you have a airplane RC shop close by, there was a paint called Clear Dope that they used on the paper wings of the plane kits back in the day.

Do you want the wood grain to show, like a vintage board, or do you want to paint it to simulate a fiberglass board? I assume the latter, but just making sure.

If you want it to appear as "wood", a mahogany stain would be appropriate for a really old Hawaiian style longboard. Probably no stain at all to simulate a later balsa board. Balsa is extremely porous and will soak up the finish coat, emphasizing the too-large-for-scale grain. Many coats of clear urethane or lacquer, sanded in between, will fill the grain and make a fairly convincing job.

If you want to simulate a glass board, make sure it's very well dried to get it to shrink as much as possible. Oven drying is a good option. Personally, I would choose a two-part polyester or ( second choice ) urethane primer....bury it. When you sand it, be sure to re-prime any areas that get thin or have wood show-through. Wood moves and shrinks over time, and any thin spots in the primer will come back to haunt you.